Dividing zero

When working modulo some number n we call two integers divisors of zero if their product is 0. For example, 2 and 3 are divisors of zero when working modulo 6. So are 4 and 3 ( \(3 \times 4=12 \equiv 0 \pmod{6} ) \). Thus, there are 3 zero divisors when working modulo 6: 2, 3, and 4.

How many zero divisors exist when working modulo 8192?

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